"Science Stays True Here" Journal of Mathematics and Statistical Science (ISSN 2411-2518, USA), Vol.6, issues 5, 182-186 | Science Signpost Publishing Analytical Study of Hilbert Space and Algebra of Operators U.K. Srivastava1, L.K. Roy2, Binod Prasad3, C.D. Pathak4, & Surendra Ray5 Department of Mathematics 1. R.S.S. College, Chochahan, P.O.:- Aniruddh Belsar, Dist.- Muzaffarpur – 844111, B.R.A. Bihar University, Muzaffarpur – 842001, Bihar, India. 2. T.P. Varma College, Narkatiaganj, West Champaran – 845455 , B.R.A. Bihar University, Muzaffarpur – 842001 , Bihar, India. 3. T.R.M. Campus, Birganj, Parsa, Nepal, Tribhuvan University, Nepal. 4. R.R.M. Campus, Janakpurdham, Nepal, Tribhuvan University, Nepal. 5. R.R.M. Campus, Janakpurdham, Nepal, Tribhuvan University, Nepal. E-mail:
[email protected] Abstract This present paper deals with the study of Hilbert Space and Algebra of Operators. Here, we consider R as additive group of reals with discrete topology and several ways of constructing C* - algebras Canonically associated with R and π, The Universal representation of R on Hilbert Space H, it is proved in this paper that all C*- algebras homomorphism and representation will be * - preserving Keywords: Hilbert space, Tensor product, C* - tensor norms, C* - algebras, Normal and Binormal norms, W*- algebras. Introduction E.G. Effros (1) and Kothe (3,4) are the pioneer workers of the present area. In fact, the present work is the extension of work done by Halub, J.R. (2), Kumar et al. (5), Kumar et al. (6), Kumar et al. (7), Srivastava et al. (8), Srivastava et al. (9), Srivastava et al.